He also said India and US will continue to expand their military exercises and maritime cooperation so that the two forces become "interoperable".
Mr Obama said during his visit to India last year, Prime Minister Narendra Modi and he agreed to a new joint vision for the Asia Pacific and Indian Ocean region.
"It's rooted in our shared interests in a region that's peaceful and prosperous and where all countries play by the same rules, in accordance with international law and norms, including freedom of navigation," Mr Obama said in an interview to PTI.
The Asia Pacific region has witnessed tension after China flexed its military muscle in the resource-rich South China Sea.
The South China Sea is also a major shipping lane. Over half of the world's commercial shipping passes through the Indo-Pacific waterways.
China claims almost the whole of the South China Sea, resulting in overlapping claims with several other Asian nations like Vietnam and the Philippines, Malaysia and Brunei.
They accuse China of illegally reclaiming land in contested areas to create artificial islands with facilities that could potentially be for military use.
The US has criticised Beijing for building artificial islands in the disputed sea, and has flown a B-52 bomber and sailed a guided-missile destroyer near some of the constructions China has made in recent months.
Mr Obama also said the US recognises that the Indian Ocean is vital to the security of the region and the global economy.
"Our vision recognises that the Indian Ocean is vital to the security of the region and the global economy. And it welcomes India's determination to 'Act East' with stronger security and economic partnerships across the region," the US President said.
He was replying to a question as to what role he sees for India in the emerging security situation in the Asia Pacific given what is happening and the nuclear tests by North Korea.
"We have elevated our trilateral cooperation with Japan, including on disaster response and humanitarian assistance. And we very much welcome India's increased ties with the region.
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